Computational modelling of the rheological response of wormlike micellar solutions in simple and complex deformations: flow past a sphere and contraction-expansion flow

In this work, novel numerical solutions are provided on the flow of wormlike micellar solutions in both banding and non-banding regimes, in complex benchmark flows, such as flow past a sphere and a modified Couette contraction-expansion flow. The model used here is the latest model-variant of the Bautista-Manero-Puig family of constitutive equations, i.e. the BMP+_τ_p model [1-3]. The properties of this micellar rheological equation-of-state are exposed in simple ideal deformations, such as steady simple shear and uniaxial extension. Solutions in complex flow, in benchmark flow past-a-sphere and a modified contraction-expansion geometries, are obtained with our hybrid finite volume/element algorithm and expose the influence of the thixotropic and viscoelastic features of these models in flow-structure and yield-front representations. In flow past a sphere [2], in the mode of particle settling in wormlike micelles, location of a negative-wake instability is predicted, whilst for extremely concentrated wormlike micellar solutions, fore-aft asymmetries are observed, much resembling experimental finding for the settling of particles in viscoelastic Carbopol gels. In the modified Couette contraction-expansion flow cell [1], the influence of a complex-flow deformation in a shear-banded flow is studied, for which simple shear-banding features, i.e. flow segregation, are lost in the mixed inhomogeneous shear-to-extensional deformation found in the constriction zone, and are recovered in the fully-developed flow region downstream from the constriction.